by ttt2 (version ttt2 1.15)
The rewrite relation of the following TRS is considered.
| Begin(0(x0)) | → | Wait(Right1(x0)) |
| Begin(s(x0)) | → | Wait(Right2(x0)) |
| Begin(0(x0)) | → | Wait(Right3(x0)) |
| Begin(s(x0)) | → | Wait(Right4(x0)) |
| Begin(p(s(x0))) | → | Wait(Right5(x0)) |
| Begin(s(x0)) | → | Wait(Right6(x0)) |
| Begin(s(x0)) | → | Wait(Right7(x0)) |
| Begin(0(x0)) | → | Wait(Right8(x0)) |
| Right1(twoto(End(x0))) | → | Left(p(p(s(s(s(p(p(p(s(s(s(0(p(p(s(s(End(x0)))))))))))))))))) |
| Right2(twoto(End(x0))) | → | Left(p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(End(x0)))))))))))))))))))))))))))) |
| Right3(twice(End(x0))) | → | Left(p(s(p(s(0(s(p(s(s(s(s(p(s(End(x0))))))))))))))) |
| Right4(twice(End(x0))) | → | Left(s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(End(x0))))))))))))))))))))) |
| Right5(p(End(x0))) | → | Left(p(End(x0))) |
| Right6(p(p(End(x0)))) | → | Left(p(End(x0))) |
| Right7(p(End(x0))) | → | Left(End(x0)) |
| Right8(p(End(x0))) | → | Left(0(s(s(s(s(p(s(End(x0))))))))) |
| Right1(twoto(x0)) | → | Atwoto(Right1(x0)) |
| Right2(twoto(x0)) | → | Atwoto(Right2(x0)) |
| Right3(twoto(x0)) | → | Atwoto(Right3(x0)) |
| Right4(twoto(x0)) | → | Atwoto(Right4(x0)) |
| Right5(twoto(x0)) | → | Atwoto(Right5(x0)) |
| Right6(twoto(x0)) | → | Atwoto(Right6(x0)) |
| Right7(twoto(x0)) | → | Atwoto(Right7(x0)) |
| Right8(twoto(x0)) | → | Atwoto(Right8(x0)) |
| Right1(0(x0)) | → | A0(Right1(x0)) |
| Right2(0(x0)) | → | A0(Right2(x0)) |
| Right3(0(x0)) | → | A0(Right3(x0)) |
| Right4(0(x0)) | → | A0(Right4(x0)) |
| Right5(0(x0)) | → | A0(Right5(x0)) |
| Right6(0(x0)) | → | A0(Right6(x0)) |
| Right7(0(x0)) | → | A0(Right7(x0)) |
| Right8(0(x0)) | → | A0(Right8(x0)) |
| Right1(p(x0)) | → | Ap(Right1(x0)) |
| Right2(p(x0)) | → | Ap(Right2(x0)) |
| Right3(p(x0)) | → | Ap(Right3(x0)) |
| Right4(p(x0)) | → | Ap(Right4(x0)) |
| Right5(p(x0)) | → | Ap(Right5(x0)) |
| Right6(p(x0)) | → | Ap(Right6(x0)) |
| Right7(p(x0)) | → | Ap(Right7(x0)) |
| Right8(p(x0)) | → | Ap(Right8(x0)) |
| Right1(s(x0)) | → | As(Right1(x0)) |
| Right2(s(x0)) | → | As(Right2(x0)) |
| Right3(s(x0)) | → | As(Right3(x0)) |
| Right4(s(x0)) | → | As(Right4(x0)) |
| Right5(s(x0)) | → | As(Right5(x0)) |
| Right6(s(x0)) | → | As(Right6(x0)) |
| Right7(s(x0)) | → | As(Right7(x0)) |
| Right8(s(x0)) | → | As(Right8(x0)) |
| Right1(twice(x0)) | → | Atwice(Right1(x0)) |
| Right2(twice(x0)) | → | Atwice(Right2(x0)) |
| Right3(twice(x0)) | → | Atwice(Right3(x0)) |
| Right4(twice(x0)) | → | Atwice(Right4(x0)) |
| Right5(twice(x0)) | → | Atwice(Right5(x0)) |
| Right6(twice(x0)) | → | Atwice(Right6(x0)) |
| Right7(twice(x0)) | → | Atwice(Right7(x0)) |
| Right8(twice(x0)) | → | Atwice(Right8(x0)) |
| Atwoto(Left(x0)) | → | Left(twoto(x0)) |
| A0(Left(x0)) | → | Left(0(x0)) |
| Ap(Left(x0)) | → | Left(p(x0)) |
| As(Left(x0)) | → | Left(s(x0)) |
| Atwice(Left(x0)) | → | Left(twice(x0)) |
| Wait(Left(x0)) | → | Begin(x0) |
| twoto(0(x0)) | → | p(p(s(s(s(p(p(p(s(s(s(0(p(p(s(s(x0)))))))))))))))) |
| twoto(s(x0)) | → | p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(x0)))))))))))))))))))))))))) |
| twice(0(x0)) | → | p(s(p(s(0(s(p(s(s(s(s(p(s(x0))))))))))))) |
| twice(s(x0)) | → | s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(x0))))))))))))))))))) |
| p(p(s(x0))) | → | p(x0) |
| p(s(x0)) | → | x0 |
| p(0(x0)) | → | 0(s(s(s(s(p(s(x0))))))) |
| 0(x0) | → | x0 |
| Begin(0(x0)) | → | Wait(Right1(x0)) |
| Begin(s(x0)) | → | Wait(Right2(x0)) |
| Begin(0(x0)) | → | Wait(Right3(x0)) |
| Begin(s(x0)) | → | Wait(Right4(x0)) |
| Begin(p(s(x0))) | → | Wait(Right5(x0)) |
| Begin(s(x0)) | → | Wait(Right6(x0)) |
| Begin(s(x0)) | → | Wait(Right7(x0)) |
| Begin(0(x0)) | → | Wait(Right8(x0)) |
| Right1(twoto(End(x0))) | → | Left(p(p(s(s(s(p(p(p(s(s(s(0(p(p(s(s(End(x0)))))))))))))))))) |
| Right2(twoto(End(x0))) | → | Left(p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(End(x0)))))))))))))))))))))))))))) |
| Right3(twice(End(x0))) | → | Left(p(s(p(s(0(s(p(s(s(s(s(p(s(End(x0))))))))))))))) |
| Right4(twice(End(x0))) | → | Left(s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(End(x0))))))))))))))))))))) |
| Right5(p(End(x0))) | → | Left(p(End(x0))) |
| Right6(p(p(End(x0)))) | → | Left(p(End(x0))) |
| Right7(p(End(x0))) | → | Left(End(x0)) |
| Right8(p(End(x0))) | → | Left(0(s(s(s(s(p(s(End(x0))))))))) |
| Right1(twoto(x0)) | → | Atwoto(Right1(x0)) |
| Right2(twoto(x0)) | → | Atwoto(Right2(x0)) |
| Right3(twoto(x0)) | → | Atwoto(Right3(x0)) |
| Right4(twoto(x0)) | → | Atwoto(Right4(x0)) |
| Right5(twoto(x0)) | → | Atwoto(Right5(x0)) |
| Right6(twoto(x0)) | → | Atwoto(Right6(x0)) |
| Right7(twoto(x0)) | → | Atwoto(Right7(x0)) |
| Right8(twoto(x0)) | → | Atwoto(Right8(x0)) |
| Right1(0(x0)) | → | A0(Right1(x0)) |
| Right2(0(x0)) | → | A0(Right2(x0)) |
| Right3(0(x0)) | → | A0(Right3(x0)) |
| Right4(0(x0)) | → | A0(Right4(x0)) |
| Right5(0(x0)) | → | A0(Right5(x0)) |
| Right6(0(x0)) | → | A0(Right6(x0)) |
| Right7(0(x0)) | → | A0(Right7(x0)) |
| Right8(0(x0)) | → | A0(Right8(x0)) |
| Right1(p(x0)) | → | Ap(Right1(x0)) |
| Right2(p(x0)) | → | Ap(Right2(x0)) |
| Right3(p(x0)) | → | Ap(Right3(x0)) |
| Right4(p(x0)) | → | Ap(Right4(x0)) |
| Right5(p(x0)) | → | Ap(Right5(x0)) |
| Right6(p(x0)) | → | Ap(Right6(x0)) |
| Right7(p(x0)) | → | Ap(Right7(x0)) |
| Right8(p(x0)) | → | Ap(Right8(x0)) |
| Right1(s(x0)) | → | As(Right1(x0)) |
| Right2(s(x0)) | → | As(Right2(x0)) |
| Right3(s(x0)) | → | As(Right3(x0)) |
| Right4(s(x0)) | → | As(Right4(x0)) |
| Right5(s(x0)) | → | As(Right5(x0)) |
| Right6(s(x0)) | → | As(Right6(x0)) |
| Right7(s(x0)) | → | As(Right7(x0)) |
| Right8(s(x0)) | → | As(Right8(x0)) |
| Right1(twice(x0)) | → | Atwice(Right1(x0)) |
| Right2(twice(x0)) | → | Atwice(Right2(x0)) |
| Right3(twice(x0)) | → | Atwice(Right3(x0)) |
| Right4(twice(x0)) | → | Atwice(Right4(x0)) |
| Right5(twice(x0)) | → | Atwice(Right5(x0)) |
| Right6(twice(x0)) | → | Atwice(Right6(x0)) |
| Right7(twice(x0)) | → | Atwice(Right7(x0)) |
| Right8(twice(x0)) | → | Atwice(Right8(x0)) |
| Atwoto(Left(x0)) | → | Left(twoto(x0)) |
| A0(Left(x0)) | → | Left(0(x0)) |
| Ap(Left(x0)) | → | Left(p(x0)) |
| As(Left(x0)) | → | Left(s(x0)) |
| Atwice(Left(x0)) | → | Left(twice(x0)) |
| Wait(Left(x0)) | → | Begin(x0) |
| twoto(0(x0)) | → | p(p(s(s(s(p(p(p(s(s(s(0(p(p(s(s(x0)))))))))))))))) |
| twoto(s(x0)) | → | p(p(s(s(p(p(p(s(s(s(twice(p(p(s(s(p(p(p(s(s(s(twoto(p(s(p(s(x0)))))))))))))))))))))))))) |
| twice(0(x0)) | → | p(s(p(s(0(s(p(s(s(s(s(p(s(x0))))))))))))) |
| twice(s(x0)) | → | s(p(p(p(p(s(s(s(s(s(twice(p(s(p(s(p(s(p(s(x0))))))))))))))))))) |
| p(p(s(x0))) | → | p(x0) |
| p(s(x0)) | → | x0 |
| p(0(x0)) | → | 0(s(s(s(s(p(s(x0))))))) |
| 0(x0) | → | x0 |